Contents Online
Mathematical Research Letters
Volume 25 (2018)
Number 2
Purity of critical cohomology and Kac’s conjecture
Pages: 469 – 488
DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n2.a6
Author
Abstract
We provide a new proof of the Kac positivity conjecture for an arbitrary quiver $Q$. The ingredients are the cohomological integrality theorem in Donaldson–Thomas theory, dimensional reduction, and an easy purity result. These facts imply the purity of the cohomological Donaldson–Thomas invariants for partially nilpotent representations of a quiver with potential $(\widetilde{Q},W)$ associated to $Q$, which in turn implies positivity of the Kac polynomials for $Q$.
Received 27 January 2014
Accepted 21 April 2017
Published 5 July 2018